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vodomira [7]
3 years ago
15

A curve passes through the point (0,7) and has the property that the slope of the curve at every point P is five times the y-coo

rdinate of P. What is the equation of the curve
Mathematics
1 answer:
iren [92.7K]3 years ago
8 0

Answer:

y(x) = 7e^(5x)

Step-by-step explanation:

The question says that the slope of the curve at every point P is five times the y-coordinate of P. This means that

dy/dx = 5y

Refer to solutions of differential equations, dy/dt = ky, being in the form of y(t) = y(0) e^(kt)

Using the above stated law now, we can relate to our equation, saying that

y(x) = y(0) e^(5x)

The point given from the question is, (0, 7). This also means that y(0) = 7. So finally, we can have

y(x) = 7e^(5x)

And that is our needed equation of the curve

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27% of the students in a school are in grade 6. This is 540 students. How many students are in the school?
Anettt [7]

There are a total of 2,000 students in the school.

1.) There are 540 students in the 6th grade. 540 is only 27% of students compared to the total. To find the total students in the whole school, we divide 540 by 27%.

2.) We first change 27% into a decimal by moving the point two times to the left. (Rule to change the percent into a decimal)

27% = .27

3.) Before we divide, we remove the decimal by moving the decimal two times to the right and so do we to 540.

.27 = 27

540. = 54000.

4.) Now we have 54000 divided by 27 which give us the answer of 2,000.

Hope this Helps!!!

Please Mark as Brainliest!!!

6 0
3 years ago
Shoes were 20% off the sale price was 19.60 what is the original price?
Amanda [17]
I believe the answer is 23.52 because if u add 19.60 to 20% thats what u get
6 0
3 years ago
Summation notation of 2+4+6+8+10
Veronika [31]
The answer to this question is 30.
4 0
4 years ago
Set up and solve the following using dimensional analysis.
Softa [21]
1).  Multiply (5400 inches) by (1 foot / 12 inch) then by (1 mile / 5280 foot).

      (See explanation at the bottom)

         =      (5400 inch) x (1 foot / 12 inch) x (1 mile / 5280 foot)

         =      (5400 x 1 x 1 / 12 x 5280)  (inch - foot - mile / inch - foot) 

         =          0.0852  mile  


2).  Multiply (16 week) by (7 day/week) then by (24 hour/day)
       then by (60 minute/hour) then by (60 sec/minute).

3).  Multiply (54 yards) by (3 foot/yard) then by (1 meter/3.28 foot)
       and then by (1000 mm/meter)

4).  Multiply (36 cm/second) by (3600 second/hour) then by (1 meter/100 cm)
      then by (1 mile/1609.3 meter).

5).  Look up how many grams in a pound  ('P')
       Look up how many mL in a gallon       ('G')

      Multiply (1.09 g/mL) by ( 1 pound/ P gram) then by (1 gallon/ G mL)

6).  Multiply (32 foot/sec) by (1 meter / 3.28 foot) then by (60 sec/minute).


Each time I told you to multiply by something, it was always a fraction
where the numerator and denominator are equal, like (60 seconds/minute)
or (1 foot / 12 inch).  Since the top and bottom of the fraction are equal, the
value of the fraction is ' 1 ' , and multiplying by it doesn't change the value,
it only changes the units ... that's what this whole exercise is about.
When you multiply, KEEP the units in the product, and then, after you multiply, you can 'cancel' units out of the top and bottom of the product.
Like if you have 'feet' on top and bottom, just cross them out.  When you're done, if you did it correctly, the last unit you end up with will be the one you want.      
4 0
3 years ago
If 'a' is a number lying between 0 and 1. then which of the following is in increasing order? a) a², a, √a b) a √a ,a² c) a²,√a,
viktelen [127]

Step-by-step explanation:

None of these,

a(under root),a, a(square)

this is the correct answer

5 0
3 years ago
Read 2 more answers
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